1. Measurement of nuclear radius
Four methods outlined for charge matter radius:
Diffraction scattering
Atomic x-rays
Muonic x-rays
Mirror Nuclides

2. Measurement of nuclear radius
Three methods outlined for nuclear matter radius:
Rutherford scattering
Alpha particle decay
-mesic x-rays

3. Diffraction scattering
q = momentum transfer

4. Diffraction scattering
Measure the scattering intensity as a function of  to infer the distribution of charge in the nucleus,

5. Diffraction scattering
Measure the scattering intensity as a function of  to infer the distribution of charge in the nucleus
is the inverse Fourier transform of
is known as the form factor for the scattering.
c.f. Figure 3.4; what is learned from this?

6. Diffraction scattering
Density of electric charge in the nucleus is ≈ constant

7. Diffraction scattering
The charge distribution does not have a sharp boundary
Edge of nucleus is diffuse - “skin”
Depth of the skin ≈ 2.3 f
RMS radius is calculated from the charge distribution and, neglecting the skin, it is easy to show

8. Atomic X-rays Assume the nucleus is uniform charged sphere.
Potential V is obtained in two regions:
Inside the sphere
Outside the sphere

9. Atomic X-rays
For an electron in a given state, its energy depends on -
Assume does not change appreciably if Vpt Vsphere
Then, E = Esphere - Ept
Assume can be giving (3.12)

10. Atomic X-rays E between sphere and point nucleus for
Compare this E to measurement and we have R.
Problem!
We will need two measurements to get R --
Consider a 2p 1s transition for (Z,A) and (Z,A’) where
A’ = (A-1) or (A+1) ; what x-ray does this give?

11. Atomic X-rays Assume that the first term will be ≈ 0. Why?
Then, use E1s from (3.13) for each E1s term. Why?

12. Atomic X-rays
This x-ray energy difference is called the “isotope shift”
We assumed that R = Ro A1/3. Is there any authentication?
How good does your spectrometer have to be to see the effect?
We assumed we could use hydrogen-line 1s wavefunctions Are these good enough to get good results?
Can you use optical transitions instead of x-ray transitions?

13. Muonic X-rays Compare this process with atomic (electronic) x-rays:
Similarities
Differences
Advantages
Disadvantages
What is ao ?
Pauli Exclusion principle for muons, electrons?

14. Coulomb Energy Differences
Calaulate the Coulomb energy of the charge distribution directly
Consider mirror nuclides:
Measure EC; How?
Assume R is same for both nuclides. Why?

15. Measurement of nuclear radius
Three methods outlined for nuclear matter radius:
Rutherford scattering
Alpha particle decay
-mesic x-rays